Question

30. If the chords of contact of tangents from two points (x1, yı) and (x2, y2) to the hyperbola 4x2 - 9y2 - 36 = 0 are at right angles, then x1x2/y1y2 is equal to :
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Answer 1

Step-by-step explanation:

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Answer 2

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=>. -81/16

The equation of hyperbola is

4x² - 9y² = 36

=> x²/9 - y²/4 = 1 ....(1)

The equation of the chords of contact of tangents from two points (x1, yı) and (x2, y2) to the given hyperbola are

xx1/9 - yy1/4 = 1 ....(2)

and xx2/9 - yy2/4 = 1 ....(3)

Lines (2) and (3) are at right angles

4/9.x1/y1 × 4/9.x2/y2 = -1 (m1m2=-1)

=> x1x2/y1y2 = -(9/2)²

= -81/16

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